Numerical analysis of flow and forced convection heat transfer of non-Newtonian fluid in a pipe based on fractional constitutive model

Abstract

Purpose This paper aims to use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process. Design/methodology/approach This paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent. Findings This paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity. Research limitations/implications First, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil. Originality/value This study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail.

Guest editorial

“…After comprehensive peer review, only one third papers qualified for acceptance for final publication. This special issue comprises the theoretical and experimental research articles that elucidate the research efforts and recent developments on “New Trends in Heat and Fluid Flow: Applications and Recent Developments.” This issue consists of (Agrawal et al , 2021; Akbari et al , 2021; Alanazi et al , 2021; Alkanhal, 2021; Chang et al , 2021; Chen et al , 2021; Dehghan et al , 2021; Hayat et al , 2021; Riaz et al , 2021; Saadun et al , 2021; Safdari Shadloo, 2020; Selimefendigil and Öztop, 2021; Ullah et al , 2021; Xing et al , 2021; Yilmaz, 2021; Youjun et al , 2020; Zaher et al , 2021; Zhang et al , 2020) accepted papers related to fluid dynamics; heat exchangers; heat transfer enhancement; heat and mass transfer in thermal energy; heat and mass transfer in porous media; heat transfer phenomena in biological systems; nanofluids; two-phase/multiphase flows; Newtonian and non-Newtonian fluids; thermodynamics; and numerical simulations and methods. The presented results are discussed with an adequate physical interpretation.…”

On Thermal Distribution for Darcy–Forchheimer Flow of Maxwell Sutterby Nanofluids over a Radiated Extending Surface

“…Analysis on change of viscosity, and thus the behavior of non-Newtonian fluids, was conducted by Shende et al [ 1 ]. The heat transmit by forced convection of a non-Newtonian liquid in a fractional constitutive version boundaries based on a pipe was examined by Chang et al [ 2 ]. For the result of non-Newtonian fluid flow, simulations for the time-lattice for Boltzmann process paradigm were taken by Bisht et al [ 3 ].…”

Review on shear thickening fluid and its applications in vibration reduction

“…a) shows the relationship between viscous shear stress and velocity gradient under different yield stresses and fractional derivative orders. It can be seen from the figure that different types of non-Newtonian fluids, including shear thickening fluids, can be clearly characterized by using this model.Using equation (8) as a foundation, Chang et al[100] developed a viscosity constitutive relation for non-Newtonian fluids within pipelines, which is presented in equation(10).…”